Publication Date
2025
Document Type
Dissertation/Thesis
First Advisor
Geline, Michael
Degree Name
Ph.D. (Doctor of Philosophy)
Legacy Department
Department of Mathematical Sciences
Abstract
In this dissertation, we examine the existence of positive height Knörr RD-lattices for D an elementary abelian p-group and R an unramified extension of the p-adics Zp. Knörr lattices form an important subclass of the absolutely indecomposable lattices and have close connections to modular representation theory’s “local to global” behavior. We generalize many prior results, shown only when p = 2, to odd p when |D| = p3. Further, when p = 3, we show that a positive height Knörr RD lattice must have a projective summand when restricted to any maximal subgroup of D. The proof of this requires techniques completely separate to the p = 2 case. We use this result to demonstrate that there does not exist a positive height Knörr RD-lattice for the elementary abelian group of order 27 of rank less than 30. Our second main result shows that when eiRD is a DVR for each KD idempotent ei, then the lattice whose character has “too much” multiplicity of any one irreducible component must decompose. This gives us a useful restriction of the characters a non-cyclic Knörr RD-lattice can afford.
Recommended Citation
Swartz, Marie, "Knörr Lattices for Elementary Abelian Groups Over Unramified Extensions of Z_p" (2025). Graduate Research Theses & Dissertations. 8093.
https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/8093
Extent
78 pages
Language
en
Publisher
Northern Illinois University
Rights Statement
In Copyright
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.
Media Type
Text
